def main(close=True, show=True, save=False):
"""Generate all plots.
args
close: close any open plots.
show: display new plots on screen
save: write new plots to a file
returns
None
"""
print(f"\nRunning module \"{__name__}\" ...")
N = c.num_days()
print("There are a total of %d days" % (N))
print("The earleiest date is %s" % (c.ind2datetime(0)))
print("The latest date is %s" % (c.ind2datetime(N-1)))
if close:
_num = c.next_fig_num(close)
close = False
s.main(close=close, show=show, save=save)
ts.main(close=close, show=show, save=save)
rs.main(close=close, show=show, save=save)
fr.main(close=close, show=show, save=save)
lp.main(close=close, show=show, save=save)
hp.main(close=close, show=show, save=save)
bp.main(close=close, show=show, save=save)
dr.main(close=close, show=show, save=save)
def main(close=True, show=True, save=False, file_names=("Fig9.pdf",)):
"""Plots to be used in the paper."""
print(f"\nRunning module \"{__name__}\" ...")
cases = c.get_data("cases", "US")
cases_padded, pad_sz = c.extrapolate(cases)
f0, f1 = 1/7.0, 1/8.0
y_el_1 = ellip_bf(cases_padded, f0, f1)[pad_sz:-pad_sz]
H = ellip_spec(f0, f1, 1024)
y_fft_1 = c.apply_spectrum(cases_padded, H)[pad_sz:-pad_sz]
start = 40
print("plot #1 begins on date: %s" % c.ind2datetime(start))
y_label = lambda x, p: "%.0fk" % (x/1000)
x = np.arange(0, max(cases[start:].shape), 1)
dz = np.zeros(len(x))
num = c.next_fig_num(close)
fig, (ax3) = plt.subplots(1, 1, figsize=(5, 3.294), num=num)
ax3.fill_between(x, cases[start:], dz, alpha=0.1, color="#000000", label="daily cases")
ax3.plot(x, y_el_1[start:], linewidth=1.25, label="elliptic high-pass #1", linestyle=(0,(2,1)))
ax3.plot(x, y_fft_1[start:], linewidth=1.25, label="FFT high-pass #1", linestyle=(0,(9,9)))
ax3.set(xlabel='time [days]', ylabel='daily new cases')
ax3.get_yaxis().set_major_formatter(ticker.FuncFormatter(y_label))
ax3.grid(True, alpha=0.2)
ax3.axis([min(x), max(x), -15000, 80000])
ax3.legend(loc='upper left', prop={'size': 9}, handlelength=2)
plt.tight_layout()
if show:
plt.show(block=False)
if save:
c.save_fig(fig, file_names[0])
def main(N=3, close=True, show=True, save=False, file_names=("Fig3.pdf", )):
"""Reconstruct the waveform with 1, 2, or 3 sinusoids. Then search
for min and max, provided that the harmonics sufficiently big.
args
N (int): The number of harmonics to consider (1, 2, or 3).
close (bool): True if existing plots will be closed.
show (bool): True if the plot will be displayed on screen.
save (bool): True if the plot will be saved to file.
returns
None
"""
print(f"\nRunning module \"{__name__}\" ...")
# some input variables
start = 70
end = c.num_days(
) - 5 # allowing five days for revisions to be made to the repo
fft_pts = 2**19
print("Analysis date range: %s - %s" %
(c.ind2datetime(start), c.ind2datetime(end)))
print("Analysis window size: %d" % (end - start))
print("FFT size: 2^%d = %d points" % (np.log2(fft_pts), fft_pts))
# The frequencies we are interested in.
f = np.array([[1 / 7, 2 / 7, 3 / 7]])[:, :N]
# List of countries to be included in the plots and print out.
countries = ["US", "Mexico", "Argentina", "United Kingdom", "Brazil"]
# The datetime at which the integrated derivative begins (time is 12:00 noon).
t_ref = c.ind2datetime(
start) # for FFT derivative plus symbolic integration
print("Reference time for the integrated derivative: %s" % t_ref)
num_days = 21 # number of days to synthesize
step_sz = 20 / (24 * 60 * 60) # step size for synthesis (20 seconds)
xs = np.array([np.arange(0, num_days,
step_sz)]) # time-axis for calculating sinusoids
x = xs[0] + c.days2decimals(t_ref) # time-axis for plotting sinusoids
print("Step size for resynthesis: %1.4f seconds" %
(step_sz * 24 * 60 * 60))
print()
# This will be the main data object of interest.
phf = {"cases": dict(), "deaths": dict()}
for rt in phf:
for country in countries:
data = c.get_data(rt, "global", country=country, state=None)
d_dt_data = c.deriv_fft(data)[start:end] # FFT derivative
Z = np.fft.fft(d_dt_data,
n=int(fft_pts)) / fft_pts # spectrum of derivative
H_f = Z[(fft_pts * f + 0.5).astype(np.int)] # freqs. of interest
theta = np.angle(H_f) # phase angles
m = np.abs(H_f) # magnitudes
y = (m / (2 * np.pi * f)) * np.sin(
2 * np.pi * xs.T * f + theta) # Compute integrated sinusoids
y_sum = np.sum(y, 1) # Sum sinusoids
y_sum = y_sum - (np.max(y_sum) +
np.min(y_sum)) / 2 # align vertically for plot
y_sum = y_sum / max(np.abs(y_sum)) # normalize for plot
phf[rt][country] = y_sum # Collect the data
# Text summary of results
text_summary(phf, t_ref, xs)
# Plot
if show or save:
make_plot(phf,
x,
countries,
close=close,
show=show,
save=save,
file_name=file_names[0])
def main(close=True,
show=True,
save=False,
file_names=(
"Fig10.pdf",
"Fig11.pdf",
"FigUnused_BP.pdf",
)):
"""Plots to be used in the paper."""
print(f"\nRunning module \"{__name__}\" ...")
cases = c.get_data("cases", "US")
deaths = c.get_data("deaths", "US")
# Extrapolation
cases_padded, pad_sz = c.extrapolate(cases)
deaths_padded, pad_sz = c.extrapolate(deaths)
numPts = 1024
# first plot
wp, ws = [1 / 8.0, 1 / 6.0], [1 / 9.0, 1 / 5.0]
y_el_1 = ellip_bf(cases_padded, wp, ws)[pad_sz:-pad_sz] # elliptic
H_1 = ellip_spec(wp, ws, numPts)
y_fft_1 = c.apply_spectrum(cases_padded, H_1)[pad_sz:-pad_sz] # FFT
start1 = 40
print("plot #1 begins on date: %s" % c.ind2datetime(start1))
y1_lables = lambda x, p: "%.0fk" % (x / 1000)
x1 = np.arange(0, max(cases[start1:].shape), 1)
dz = np.zeros(len(x1))
num = c.next_fig_num(close)
fig1, (ax1) = plt.subplots(1, 1, figsize=(5, 3.294), num=num)
ax1.fill_between(x1,
cases[start1:],
dz,
alpha=0.1,
color="#000000",
label="daily deaths")
ax1.plot(x1,
y_el_1[start1:],
linewidth=1.25,
label="elliptic band-pass #1",
linestyle=(0, (2, 1)))
ax1.plot(x1,
y_fft_1[start1:],
linewidth=1.25,
label="FFT band-pass #1",
linestyle=(0, (9, 9)))
ax1.get_yaxis().set_major_formatter(ticker.FuncFormatter(y1_lables))
ax1.grid(True, alpha=0.2)
ax1.legend(loc='upper left', prop={'size': 9}, handlelength=2)
ax1.set(xlabel='time [days]')
ax1.set(ylabel='daily new cases')
ax1.axis([0, max(y_fft_1[start1:].shape) - 1, -15000, 80000])
plt.tight_layout()
# second plot
wp, ws = [1 / 19, 1 / 9.0], [1 / 21.0, 1 / 8.0]
y_el_2 = ellip_bf(deaths_padded, wp, ws)[pad_sz:-pad_sz] # elliptic
H_2 = ellip_spec(wp, ws, numPts)
y_fft_2 = c.apply_spectrum(deaths_padded, H_2)[pad_sz:-pad_sz]
start3 = 100
print("plot #2 begins on date: %s" % c.ind2datetime(start3))
y3_lables = lambda x, p: "%.1fk" % (x / 1000)
x3 = np.arange(0, max(deaths[start3:].shape), 1)
dz = np.zeros(len(x3))
num += 1
fig3, (ax3) = plt.subplots(1, 1, figsize=(5, 3.3), num=num)
ax3.fill_between(x3,
deaths[start3:],
dz,
alpha=0.1,
color="#000000",
label="daily deaths")
ax3.plot(x3,
y_el_2[start3:],
linewidth=1.25,
label="elliptic band-pass #2",
linestyle=(0, (2, 1)))
ax3.plot(x3,
y_fft_2[start3:],
linewidth=1.25,
label="FFT band-pass #2",
linestyle=(0, (9, 9)))
ax3.get_yaxis().set_major_formatter(ticker.FuncFormatter(y3_lables))
ax3.grid(True, alpha=0.2)
ax3.legend(loc='upper right', prop={'size': 9}, handlelength=2)
ax3.set(xlabel='time [days]')
ax3.set(ylabel='daily new deaths')
ax3.axis([0, max(y_fft_2[start3:].shape) - 1, -250, 2500])
plt.tight_layout()
# third plot - To check if second plot contains any energy leaking
# in from bandwidth associated with the seven-day oscillation.
f = np.arange(0, numPts) / numPts
d_dt_deaths = c.deriv_fft(deaths)
Z = np.abs(np.fft.fft(d_dt_deaths, n=int(numPts)) / numPts)
norm_val = np.max(
Z[int(numPts * 0.1 +
0.5):int(numPts * 0.5 +
0.5)]) # normalize to max value above 0.1 and 0.5
Z_deaths = Z / norm_val
dz = np.zeros(len(f))
num += 1
sbStyle = (0, (1, 1))
pbStyle = (0, (2, 1))
fig4, (ax4) = plt.subplots(1, 1, figsize=(6, 3.3), num=num)
ax4.plot(np.array([wp[0]] * 2),
np.array([-999, 999]),
'#666666',
linewidth=1.25,
linestyle=pbStyle,
label="\"pass-band\"")
ax4.plot(np.array([wp[1]] * 2),
np.array([-999, 999]),
'#666666',
linewidth=1.25,
linestyle=pbStyle)
ax4.plot(np.array([ws[0]] * 2),
np.array([-999, 999]),
'#bbbbbb',
linewidth=1.25,
linestyle=sbStyle,
label="\"stop-band\"")
ax4.plot(np.array([ws[1]] * 2),
np.array([-999, 999]),
'#bbbbbb',
linewidth=1.25,
linestyle=sbStyle)
ax4.fill_between(f,
Z_deaths,
dz,
label="full spectrum",
color="#555500",
alpha=0.1)
ax4.plot(f,
Z_deaths * np.abs(H_2),
label="plotted spectrum",
linewidth=1.25,
linestyle=(0, ()))
ax4.set(title="The spectrum plotted for \"Band-Pass #2\"",
xlabel='frequency [1/day]',
ylabel='magnitude [1]')
ax4.title.set_size(10)
ax4.axis([0, 0.5, -0.0, 1.05])
ax4.legend(loc='upper right',
prop={'size': 9},
handlelength=2,
framealpha=0.92)
plt.tight_layout()
if show:
plt.show(block=False)
if save:
c.save_fig(fig1, file_names[0])
c.save_fig(fig3, file_names[1])
c.save_fig(fig4, file_names[2])
def main(close=True, show=True, save=False, file_names=("Fig1.pdf",)):
"""Create and save frequency spectrum plot for time series (deaths
and cases)."""
print(f"\nRunning module \"{__name__}\" ...")
# some variables
# countries = ["United Kingdom", "Brazil", "US", "Mexico", "South Africa", "Russia"]
# countries = ["United Kingdom", "Brazil", "US", "Mexico", "Argentina", "Kenya"]
countries = ["United Kingdom", "Brazil", "US", "Mexico", "Argentina", "Switzerland"]
start = 65
end = c.num_days()
print("total days: %d, date range: %s, %s" % (end-start, c.ind2datetime(start), c.ind2datetime(end)))
print("end-start/7 = %f, (end-start)/3.5 = %f" % ((end-start)/7.0, (end-start)/3.5))
# Create the data
p_data = dict()
for country in countries:
cases = c.get_data("cases", "global", country=country)
deaths = c.get_data("deaths", "global", country=country)
f, Z_cases = process_data(cases, start, end)
f, Z_deaths = process_data(deaths, start, end)
p_data[country] = {"cases": Z_cases, "deaths": Z_deaths, "f": f}
# Plot the data
axis = [0, 0.5, -0.0, 1.05]
num = c.next_fig_num(close)
fig = plt.figure(figsize=(10.25, 3), num=num)
fStyle = (0,(1,1))
for row in range(2):
for col in range(3):
country = countries[col + row*3]
sub_p_data = p_data[country]
Z_cases = sub_p_data["cases"]
Z_deaths = sub_p_data["deaths"]
f = sub_p_data["f"]
ax0 = plt.subplot2grid((2, 3), (row, col), colspan=1)
ax0.plot(np.array([1/7, 1/7]), np.array([-999, 999]), '#bbbbbb', linewidth=1.0, linestyle=fStyle)
ax0.plot(np.array([2/7, 2/7]), np.array([-999, 999]), '#bbbbbb', linewidth=1.0, linestyle=fStyle)
ax0.plot(np.array([3/7, 3/7]), np.array([-999, 999]), '#bbbbbb', linewidth=1.0, linestyle=fStyle)
ax0.plot(f, Z_cases, label="cases", linewidth=1.25)
ax0.plot(f, Z_deaths, label="deaths", linewidth=1.25, linestyle=(0,(7,1)))
ax0.set(title=country)
ax0.title.set_size(10)
ax0.get_xaxis().set_tick_params(direction='in')
ax0.get_yaxis().set_tick_params(direction='in')
ax0.axis(axis)
if row == 1:
ax0.set(xlabel='frequency [1/day]')
else:
ax0.set_xticklabels('')
if col == 0:
ax0.set(ylabel='magnitude')
else:
ax0.set_yticklabels('')
if (row, col) == (0, 2):
ax0.legend(bbox_to_anchor=(1.05, 1.3), loc='upper right', prop={'size': 9}, handlelength=2, framealpha=0.92)
plt.tight_layout()
if show:
plt.show(block=False)
if save:
c.save_fig(fig, file_names[0])
def main(close=True, show=True, save=False, file_names=("Fig6.pdf", "Fig7.pdf", "Fig8.pdf",)):
"""Plots to be used in the paper."""
print(f"\nRunning module \"{__name__}\" ...")
deaths = c.get_data("deaths", "US")
deaths_padded, pad_sz = c.extrapolate(deaths)
m_ave = seven_day_ave_manual(deaths_padded)[pad_sz-3:-(pad_sz-3)] # moving average
wp, ws = 1/9, 1/8
y_el_1 = ellip_bf(deaths_padded, wp, ws)[pad_sz:-pad_sz] # elliptic
H = ellip_spec(wp, ws, 1024)
y_fft_1 = c.apply_spectrum(deaths_padded, H)[pad_sz:-pad_sz] # FFT
wp, ws = 1/21, 1/19
y_el_2 = ellip_bf(deaths_padded, wp, ws)[pad_sz:-pad_sz] # elliptic
H = ellip_spec(wp, ws, 1024)
y_fft_2 = c.apply_spectrum(deaths_padded, H)[pad_sz:-pad_sz] # FFT
start = 100
print("plots #1, #2, and #3 begin on date: %s" % c.ind2datetime(start))
y_lables = lambda x, p: "%.1fk" % (x/1000)
x = np.arange(0, max(deaths[start:].shape), 1)
dz = np.zeros(len(x))
num = c.next_fig_num(close)
fig1, (ax1) = plt.subplots(1, 1, figsize=(5, 3), num=num)
ax1.fill_between(x, deaths[start:], dz, alpha=0.1, color="#000000", label="daily deaths")
ax1.plot(x, m_ave[start:], linewidth=1.25, label="moving average")
ax1.set(xlabel='time [days]', ylabel='daily new deaths')
ax1.get_yaxis().set_major_formatter(ticker.FuncFormatter(y_lables))
ax1.grid(True, alpha=0.2)
ax1.axis([min(x), max(x), 0, 2500])
ax1.legend(loc='upper right', prop={'size': 9}, handlelength=2)
plt.tight_layout()
y_lables = lambda x, p: "%.1fk" % (x/1000)
x = np.arange(0, max(deaths[start:].shape), 1)
dz = np.zeros(len(x))
num += 1
fig2, (ax2) = plt.subplots(1, 1, figsize=(5, 3), num=num)
ax2.fill_between(x, deaths[start:], dz, alpha=0.1, color="#000000", label="daily deaths")
ax2.plot(x, y_el_1[start:], linewidth=1.25, label="elliptic low-pass #1", linestyle=(0,(2,1)))
ax2.plot(x, y_fft_1[start:], linewidth=1.25, label="FFT low-pass #1", linestyle=(0,(9,9)))
ax2.set(xlabel='time [days]', ylabel='daily new deaths')
ax2.get_yaxis().set_major_formatter(ticker.FuncFormatter(y_lables))
ax2.grid(True, alpha=0.2)
ax2.axis([min(x), max(x), 0, 2500])
ax2.legend(loc='upper right', prop={'size': 9}, handlelength=2)
plt.tight_layout()
y_lables = lambda x, p: "%.1fk" % (x/1000)
x = np.arange(0, max(deaths[start:].shape), 1)
dz = np.zeros(len(x))
num += 1
fig4, (ax4) = plt.subplots(1, 1, figsize=(5, 3), num=num)
ax4.fill_between(x, deaths[start:], dz, alpha=0.1, color="#000000", label="daily deaths")
ax4.plot(x, y_el_2[start:], linewidth=1.25, label="elliptic low-pass #2", linestyle=(0,(2,1)))
ax4.plot(x, y_fft_2[start:], linewidth=1.25, label="FFT low-pass #2", linestyle=(0,(9,9)))
ax4.set(xlabel='time [days]', ylabel='daily new deaths')
ax4.get_yaxis().set_major_formatter(ticker.FuncFormatter(y_lables))
ax4.grid(True, alpha=0.2)
ax4.axis([min(x), max(x), 0, 2500])
ax4.legend(loc='upper right', prop={'size': 9}, handlelength=2)
plt.tight_layout()
if show:
plt.show(block=False)
if save:
c.save_fig(fig1, file_names[0])
c.save_fig(fig2, file_names[1])
c.save_fig(fig4, file_names[2])
def main(close=True,
show=True,
save=False,
rt="deaths",
region="global",
country="Brazil",
state=None,
file_names=("Fig2.pdf", )):
"""time segment FFT analysis.
keyword args
close: close plots (boolean)
show: show plots (boolean)
save: save plots (boolean)
rt: record type ("deaths" or "cases")
region: global or US
country: country name
state: name of US State
returns
None
"""
print(f"\nRunning module \"{__name__}\" ...")
start = 35
data = c.get_data(rt, region, country=country, state=state)
data = data[start:]
data_d_dt = c.deriv_fft(data)
winSz = 25
print("time-spectrum start date: %s" % (c.ind2datetime(start)))
print("initial window center: %s" % (c.ind2datetime(start + winSz / 2)))
print("final window center: %s" %
(c.ind2datetime(start + len(data) - 1 - winSz / 2)))
print("sliding window size: %d" % (winSz))
N = 1024 # % pts in FFT
numSamps = len(data)
numHops = numSamps - winSz # 1 sample hops (sliding window)
# set frequency range used for plotting
minFreq = 0.0
maxFreq = 0.5
minFreq_ind = int(N * minFreq + 0.5)
maxFreq_ind = int(N * maxFreq + 0.5)
# set frequency range used for normnalization
normCutMinFreq = 0.1
normCutMaxFreq = 0.5
normCutMinFreq_ind = int(N * normCutMinFreq + 0.5)
normCutMaxFreq_ind = int(N * normCutMaxFreq + 0.5)
Z = np.zeros([numHops, maxFreq_ind - minFreq_ind])
Z_hanning = np.zeros([numHops, maxFreq_ind - minFreq_ind])
Z_d_dt = np.zeros([numHops, maxFreq_ind - minFreq_ind])
b_start = 0
b_stop = winSz
for n in range(numHops):
xr = data[b_start:b_stop]
X = np.fft.fft(xr, n=N) / N
X = np.abs(X[:N // 2])
Z[n] = X[minFreq_ind:maxFreq_ind] / np.max(
X[normCutMinFreq_ind:normCutMaxFreq_ind])
xr = data[b_start:b_stop]
X = np.fft.fft(xr * np.hanning(winSz), n=N) / N
X = np.abs(X[:N // 2])
Z_hanning[n] = X[minFreq_ind:maxFreq_ind] / np.max(
X[normCutMinFreq_ind:normCutMaxFreq_ind])
xr = data_d_dt[b_start:b_stop]
X = np.fft.fft(xr, n=N) / N
X = np.abs(X[:N // 2])
Z_d_dt[n] = X[minFreq_ind:maxFreq_ind] / np.max(
X[normCutMinFreq_ind:normCutMaxFreq_ind])
b_start += 1
b_stop += 1
# clip values that exceed unity.
Z = np.clip(Z, 0, 1)
Z_hanning = np.clip(Z_hanning, 0, 1)
Z_d_dt = np.clip(Z_d_dt, 0, 1)
# interp = None # smallest size
interp = 'sinc'
colors = cm.Blues_r
# colors = cm.magma # largest size, percetual color map
# colors = cm.gray # smallest size
xMin = winSz * 0.5
xMax = winSz * 0.5 + Z.shape[0]
num = c.next_fig_num(close)
fig = plt.figure(figsize=(10.25, 2.3), num=num)
# --------------------------------------------------------------
ax0 = plt.subplot2grid((1, 3), (0, 0))
ax0.imshow(np.flipud(Z.transpose(1, 0)),
interpolation=interp,
cmap=colors,
extent=(xMin, xMax, minFreq, maxFreq),
aspect='auto')
ax0.set(xlabel='time [days]',
title="Square Window",
ylabel='frequency [1/day]')
ax0.title.set_size(10)
ax0.yaxis.set_major_locator(plt.MultipleLocator(0.1))
# --------------------------------------------------------------
ax1 = plt.subplot2grid((1, 3), (0, 1))
ax1.imshow(np.flipud(Z_hanning.transpose(1, 0)),
interpolation=interp,
cmap=colors,
extent=(xMin, xMax, minFreq, maxFreq),
aspect='auto')
ax1.set(xlabel='time [days]', title="Hanning Window")
ax1.title.set_size(10)
ax1.set_yticklabels('')
ax1.tick_params(axis=u'y', which=u'both', length=0)
# --------------------------------------------------------------
ax2 = plt.subplot2grid((1, 3), (0, 2))
ax2.imshow(np.flipud(Z_d_dt.transpose(1, 0)),
interpolation=interp,
cmap=colors,
extent=(xMin, xMax, minFreq, maxFreq),
aspect='auto')
ax2.set(xlabel='time [days]', title="Square Window of Derivative")
ax2.title.set_size(10)
ax2.set_yticklabels('')
ax2.tick_params(axis=u'y', which=u'both', length=0)
plt.tight_layout()
if show:
plt.show(block=False)
if save:
c.save_fig(fig, file_names[0])